On the large-sample minimal coverage probability of confidence intervals after model selection

• 成果类型: Article
• 署名作者: Kabaila, Paul; Leeb, Hannes
• 署名单位: La Trobe University; Yale University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214505000001140
• 发表日期: 2006
• 页码: 619-629
• 关键词: VARIABLE SELECTION; estimators; regression; inference; distributions; likelihood; rejection; regions

摘要

We give a large-sample analysis of the minimal coverage probability of the usual confidence intervals for regression parameters when the underlying model is chosen by a conservative (or overconsistent) model selection procedure. We derive an upper bound for the large-sample limit minimal coverage probability of such intervals that applies to a large class of model selection procedures including the Akaike information criterion as well as various pretesting procedures. This upper bound can be used as a safeguard to identify situations where the actual coverage probability can be far below the nominal level. We illustrate that the (asymptotic) upper bound can be statistically meaningful even in rather small samples.